Question Calculate the ratio of input and output power in decibels, given input power is $20 \mathrm{~W}$ and output power is $40 \mathrm{~W}$ .

Studdy Solution

STEP 1

Assumptions
1. The input power is $20 \mathrm{~W}$ .
2. The output power is $40 \mathrm{~W}$ .
3. The ratio of two powers expressed in decibels (dB) is calculated using the formula: $\text{Ratio in dB} = 10 \cdot \log_{10}\left(\frac{\text{Output Power}}{\text{Input Power}}\right)$

STEP 2

First, we need to find the ratio of the output power to the input power.
$\text{Power Ratio} = \frac{\text{Output Power}}{\text{Input Power}}$

STEP 3

Now, plug in the given values for the output power and the input power to calculate the power ratio.
$\text{Power Ratio} = \frac{40 \mathrm{~W}}{20 \mathrm{~W}}$

STEP 4

Calculate the power ratio.
$\text{Power Ratio} = \frac{40}{20} = 2$

STEP 5

Next, we will use the power ratio to find the ratio in decibels (dB).
$\text{Ratio in dB} = 10 \cdot \log_{10}(\text{Power Ratio})$

STEP 6

Plug in the value for the power ratio into the decibel formula.
$\text{Ratio in dB} = 10 \cdot \log_{10}(2)$

STEP 7

Calculate the logarithm of the power ratio.
$\log_{10}(2) \approx 0.3010$

STEP 8

Now, multiply the logarithm of the power ratio by 10 to find the ratio in decibels.
$\text{Ratio in dB} = 10 \cdot 0.3010$

STEP 9

Calculate the ratio in decibels.
$\text{Ratio in dB} = 10 \cdot 0.3010 = 3.01$
The ratio of the two powers expressed in decibels is approximately $3.01$ decibels.

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Question Calculate the ratio of input and output power in decibels, given input power is $20 \mathrm{~W}$ and output power is $40 \mathrm{~W}$ .

Studdy Solution

STEP 1

Assumptions
1. The input power is $20 \mathrm{~W}$ .
2. The output power is $40 \mathrm{~W}$ .
3. The ratio of two powers expressed in decibels (dB) is calculated using the formula: $\text{Ratio in dB} = 10 \cdot \log_{10}\left(\frac{\text{Output Power}}{\text{Input Power}}\right)$

STEP 2

First, we need to find the ratio of the output power to the input power.
$\text{Power Ratio} = \frac{\text{Output Power}}{\text{Input Power}}$

STEP 3

Now, plug in the given values for the output power and the input power to calculate the power ratio.
$\text{Power Ratio} = \frac{40 \mathrm{~W}}{20 \mathrm{~W}}$

STEP 4

Calculate the power ratio.
$\text{Power Ratio} = \frac{40}{20} = 2$

STEP 5

Next, we will use the power ratio to find the ratio in decibels (dB).
$\text{Ratio in dB} = 10 \cdot \log_{10}(\text{Power Ratio})$

STEP 6

Plug in the value for the power ratio into the decibel formula.
$\text{Ratio in dB} = 10 \cdot \log_{10}(2)$

STEP 7

Calculate the logarithm of the power ratio.
$\log_{10}(2) \approx 0.3010$

STEP 8

Now, multiply the logarithm of the power ratio by 10 to find the ratio in decibels.
$\text{Ratio in dB} = 10 \cdot 0.3010$

STEP 9

Calculate the ratio in decibels.
$\text{Ratio in dB} = 10 \cdot 0.3010 = 3.01$
The ratio of the two powers expressed in decibels is approximately $3.01$ decibels.

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Question Calculate the ratio of input and output power in decibels, given input power is 20 W20 \mathrm{~W}20 W and output power is 40 W40 \mathrm{~W}40 W.

Studdy Solution

STEP 1

STEP 2

First, we need to find the ratio of the output power to the input power.Power Ratio=Output PowerInput Power \text{Power Ratio} = \frac{\text{Output Power}}{\text{Input Power}} Power Ratio=Input PowerOutput Power​

STEP 3

Now, plug in the given values for the output power and the input power to calculate the power ratio.Power Ratio=40 W20 W \text{Power Ratio} = \frac{40 \mathrm{~W}}{20 \mathrm{~W}} Power Ratio=20 W40 W​

STEP 4

Calculate the power ratio.Power Ratio=4020=2 \text{Power Ratio} = \frac{40}{20} = 2 Power Ratio=2040​=2

STEP 5

Next, we will use the power ratio to find the ratio in decibels (dB).Ratio in dB=10⋅log⁡10(Power Ratio) \text{Ratio in dB} = 10 \cdot \log_{10}(\text{Power Ratio}) Ratio in dB=10⋅log10​(Power Ratio)

STEP 6

Plug in the value for the power ratio into the decibel formula.Ratio in dB=10⋅log⁡10(2) \text{Ratio in dB} = 10 \cdot \log_{10}(2) Ratio in dB=10⋅log10​(2)

STEP 7

Calculate the logarithm of the power ratio.log⁡10(2)≈0.3010 \log_{10}(2) \approx 0.3010 log10​(2)≈0.3010

STEP 8

Now, multiply the logarithm of the power ratio by 10 to find the ratio in decibels.Ratio in dB=10⋅0.3010 \text{Ratio in dB} = 10 \cdot 0.3010 Ratio in dB=10⋅0.3010

STEP 9

Calculate the ratio in decibels.Ratio in dB=10⋅0.3010=3.01 \text{Ratio in dB} = 10 \cdot 0.3010 = 3.01 Ratio in dB=10⋅0.3010=3.01The ratio of the two powers expressed in decibels is approximately 3.013.013.01 decibels.

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Question Calculate the ratio of input and output power in decibels, given input power is $20 \mathrm{~W}$ and output power is $40 \mathrm{~W}$ .

First, we need to find the ratio of the output power to the input power.
$\text{Power Ratio} = \frac{\text{Output Power}}{\text{Input Power}}$

Now, plug in the given values for the output power and the input power to calculate the power ratio.
$\text{Power Ratio} = \frac{40 \mathrm{~W}}{20 \mathrm{~W}}$

Calculate the power ratio.
$\text{Power Ratio} = \frac{40}{20} = 2$

Next, we will use the power ratio to find the ratio in decibels (dB).
$\text{Ratio in dB} = 10 \cdot \log_{10}(\text{Power Ratio})$

Plug in the value for the power ratio into the decibel formula.
$\text{Ratio in dB} = 10 \cdot \log_{10}(2)$

Calculate the logarithm of the power ratio.
$\log_{10}(2) \approx 0.3010$

Now, multiply the logarithm of the power ratio by 10 to find the ratio in decibels.
$\text{Ratio in dB} = 10 \cdot 0.3010$

Calculate the ratio in decibels.
$\text{Ratio in dB} = 10 \cdot 0.3010 = 3.01$
The ratio of the two powers expressed in decibels is approximately $3.01$ decibels.